What is the integral of x^{-1}+x^{1/3}+5/3 ?

The integral of x^{-1}+x^{1/3}+5/3 is ln|x|+3/4 x^{4/3}+5/3 x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^{-1}+x^{1/3}+5/3

\int x^{- 1} + x^{\frac{1}{3}} + \frac{5}{3} d x

ln ∣ x ∣ + \frac{3}{4} x^{\frac{4}{3}} + \frac{5}{3} x + C

Solution steps

\int x^{- 1} + x^{\frac{1}{3}} + \frac{5}{3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{- 1} d x + \int x^{\frac{1}{3}} d x + \int \frac{5}{3} d x

\int x^{- 1} d x = ln ∣ x ∣

\int x^{\frac{1}{3}} d x = \frac{3}{4} x^{\frac{4}{3}}

\int \frac{5}{3} d x = \frac{5}{3} x

= ln ∣ x ∣ + \frac{3}{4} x^{\frac{4}{3}} + \frac{5}{3} x

Add a constant to the solution

= ln ∣ x ∣ + \frac{3}{4} x^{\frac{4}{3}} + \frac{5}{3} x + C

What is the integral of x^{-1}+x^{1/3}+5/3 ?
The integral of x^{-1}+x^{1/3}+5/3 is ln|x|+3/4 x^{4/3}+5/3 x+C